Divide. Write the quotient in lowest terms. $1\dfrac{7}{9} \div \dfrac4{5} = $
Explanation: First, let's rewrite $1\dfrac7{9}$ as a fraction: $1\dfrac{7}{9} \div \dfrac4{5} =\dfrac{16}{9} \div \dfrac{4}{5}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{4}5$ is $\dfrac5{4}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{16}{9} \div \dfrac{4}5=\dfrac{16}{9}\times\dfrac5{4}$ $=\dfrac{16\times 5}{9\times 4}$ $=\dfrac{ \stackrel{4}{\cancel{16}} \times~ 5 }{ 9\times\underset{1}{\cancel{4}}} $ $=\dfrac{4\times 5}{9\times 1}$ $=\dfrac{20}{9}$ We could also write this as $2\dfrac2{9}$.